# A Quantile Estimate Based on Local Curve Fitting

## TL;DR

This paper introduces an extended regression-based method for quantile estimation, especially effective in tail regions, applicable to multiple samples, with theoretical support and real data illustrations.

## Contribution

It generalizes the RAQE method to multiple samples and provides a theoretical framework for its application and weighting scheme.

## Key findings

- Effective in tail quantile estimation
- Applicable to multiple homogeneous samples
- Supported by theoretical analysis

## Abstract

Quantile estimation is a problem presented in fields such as quality control, hydrology, and economics. There are different techniques to estimate such quantiles. Nevertheless, these techniques use an overall fit of the sample when the quantiles of interest are usually located in the tails of the distribution. Regression Approach for Quantile Estimation (RAQE) is a method based on regression techniques and the properties of the empirical distribution to address this problem. The method was first presented for the problem of capability analysis. In this paper, a generalization of the method is presented, extended to the multiple sample scenario, and data from real examples is used to illustrate the proposed approaches. In addition, theoretical framework is presented to support the extension for multiple homogeneous samples and the use of the uncertainty of the estimated probabilities as a weighting factor in the analysis.